Moreover, at high collision energies it is well established that the (charged) particle multiplicities can be described by grand canonical partition functions assuming that the system suddenly hadronizes out of a thermalized, deconfined phase (QGP) [1]}, [2]}.
While details are still under discussion (see e.g. [3]}), this observation gives straight access to particle abundances as they are solely determined by a few thermodynamical parameters like volume, temperature and chemical potentials.
Indeed, from the inspection of hadron multiplicities observed for various collision energies and spanning from \(\sqrt{s}\, = 5.13 \, A \, \mathrm {T}e\mathrm {V}\)  (top LHC energies) down to \(\sqrt{s}\)\(\;=7\)  \(\,A\)  G\(e\) V (lowest RHIC energies in collider mode) it was found that the derived freeze-out temperatures (\(T\) ) and baryo-chemical potentials (\(\mu _b\) ) all line up on a narrow band in the QCD phase diagram (see Fig. REF ).
As an example, in [4]} a phenomenological functional dependence has been reported for central collision of heavy collision systems (i.e. Au-Au or Pb-Pb) as
\(T(\sqrt{s_{\mathrm {NN}}}) =\frac{T_{\mathrm {lim}}}{\left(1+\exp \left(2.6-\ln \left(\sqrt{s_{\mathrm {NN}}}/(0.45 \cdot \mathrm {G}e\mathrm {V}\right)\right)\right)}\) 
